Density-equalizing maps for simply-connected open surfaces

Gary P. T. Choi; Chris H. Rycroft

doi:10.1137/17m1124796

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arXiv · 1704.02525

Density-equalizing maps for simply-connected open surfaces

Gary P. T. Choi·Chris H. Rycroft

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Abstract

In this paper, we are concerned with the problem of creating flattening maps of simply-connected open surfaces in $\mathbb{R}^3$. Using a natural principle of density diffusion in physics, we propose an effective algorithm for computing density-equalizing flattening maps with any prescribed density distribution. By varying the initial density distribution, a large variety of mappings with different properties can be achieved. For instance, area-preserving parameterizations of simply-connected open surfaces can be easily computed. Experimental results are presented to demonstrate the effectiveness of our proposed method. Applications to data visualization and surface remeshing are explored.

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BibTeX RIS

Gary P. T. Choi, Chris H. Rycroft. 2017-04-08. Density-equalizing maps for simply-connected open surfaces. https://doi.org/10.1137/17m1124796

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